The narrow victory sees the Citizens climb to the second spot on the league table as they keep up their PSL title challenge, while Ea Lla Koto remain 14th just above the relegation zone.
Eric Tinkler, the City coach, made several changes to his starting line-up following his side's surprise 1-0 defeat to Maritzburg United in their previous league game on Monday.
Thabo Nodada, Letsie Koapeng and Judas Moseamedi made their return to the Citizens starting line-up, while Edmilson Dove replaced suspended Tshepo Gumede in defence.
Stars coach Serame Letsoaka made three changes to the starting line-up as his side looked to bounce back to winning ways in the league after losing 2-1 to Polokwane City at home last weekend.
Thato Thlone, Sinethemba Jantjie as well as Mohammed Anas were dropped and they were replaced by Rooi Mahamutsa, Thabo Maphakisa and Katlego Mashego on the Ea Lla Koto starting line-up.
The encounter promised to be an exciting affair as the Citizens and Ea Lla Koto displayed offensive and entertaining football in the opening stages of the match.
City striker Letsie Koapeng was looking lively for the his side and the 25-year-old forced Stars goalkeeper Thela Ngobeni into two good saves from range as the home side looked to take the lead.
Shu-Aib Walters, the City shot-stopper, was also equal to the task whenever he was tested. The lanky keeper did well to stop Stars midfielder Thabo Maphakisa's effort towards the half-hour mark.
The Citizens then slowed down the tempo of the encounter and they started making smart shot passes in the Ea Lla Koto half as they looked to penetrate the visitors' defence.
However, Ea Lla Koto were happy to sit back and defend too deep with the half-time break fast approaching. The score was 0-0 at the interval following a tightly contested first-half.
The home side continued to press Ea Lla Koto in the in early stages of the second-half - with City striker Judas Moseamedi calling Ngobeni into action with an attempt which was saved by the latter.
But former South Africa under-23 international Moseamedi was not to be denied in the 62nd minute as he beat Ngobeni with a great header to hand City a well deserved lead.
Pressure was mounting on the Stars defence and they came very close to conceding again a few minutes later. But former Kaizer Chiefs academy player Ngobeni denied Aubrey Ngoma from close range.
However, Stars were able to gain control of the match towards the end of the encounter following Tebogo Potsane's late introduction by coach Letsoaka.
City then switched to defensive mood in the closing stages of the game and they contained Stars until the match referee blew the final whistle and the home side won 1-0 on the night.